Single-objective and bi-objetive parallel heuristics for the travel planning problem - Beirigo, Breno Alves (2016)
In this study we apply single-objective and bi-objective parallel heuristics to solve broad and realistic formulations of the travel planning problem. Given a travel time window and a set of destinations with their corresponding dwelling times, the goal of our single-objective approach is to find a route that produces a budget travel’s itinerary, involving flights, hotels and departure/arrival times. In turn, our bi-objective approach adds a complexity level in the problem’s formulation once we are seeking for a Pareto set of detailed travel itineraries, which are both cost and time efficient. When the sequence of cities is fixed, the single-objective version of the problem is commonly modeled in literature as a time-dependent network and the best itinerary is computed using shortest path algorithms. However, in this study, finding the order of cities that minimizes the total cost, and besides that, a set of good trade-off solutions, are also goals. Therefore, our single-objective formulation stands for a TDSPP (Time Dependent Shortest Path Problem) embedded in the TSP (Travel Salesman Problem) whereas our bi-objective formulation stands for a TDSPP embedded in a bi-objective TSP. On the first formulation we apply an ILS (Iterated Local Search) heuristic and on the second formulation we apply the NSGA-II (Nondominated Sorting Genetic Algorithm II) framework. For performance assessing, the results of both heuristics were compared to the results of corresponding exact methods with no time constraints. All test cases simulate realistic travel itineraries and run upon real-world travel data collected in advance, besides having to comply with an execution threshold of approximately 1 minute. For 285 single-objective test cases, our ILS heuristic was able to reach solutions in average less than 4.1% divergent from an exact implementation, besides reaching the optimal solution in about 30% of the test cases. In turn, for 180 bi-objective test cases, our NSGA-II implementation was able to reach an approximated solution in average up to 8% divergent from an exact implementation.